Find the centre and radius of each of the following circles.
(i) $x^{2} + y^{2} = 25$
(ii) $(x - 5)^{2} + (y - 3)^{2} = 20$
(iii) ${(x - \frac{1}{2})}^{2} + {(y + \frac{1}{3})}^{2} = \frac{1}{36}$

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Solution

Equation of circle is given by:
$(x - a)^{2} + (y - b)^{2} = r^{2}$ , where $(a, b)$ is the center and $r$ is the radius

(I) $x^{2} + y^{2} = 25$
Center $= (0, 0)$
Radius $= 5$

(ii) $(x - 5)^{2} + (y - 3)^{2} = 20$
Center $= (5, 3)$
Radius $= \sqrt{20} = 2 \sqrt{5}$

(iii) ${(x - \frac{1}{2})}^{2} + {(y + \frac{1}{3})}^{2} = \frac{1}{36}$
Center $= (\frac{1}{2}, \frac{- 1}{3})$
Radius $= \frac{1}{6}$

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Find the centre and radius of each of the following circles.(i) x2+y2=25(ii) (x−5)2+(y−3)2=20(iii) (x−12)2+(y+13)2=136

Equation of circle is given by:(x−a)2+(y−b)2=r2, where (a,b) is the center and r is the radius(I) x2+y2=25 Center =(0,0) Radius =5(ii) (x−5)2+(y−3)2=20 Center =(5,3) Radius =√20=2√5(iii) (x−12)2+(y+13)2=136 Center =(12,−13) Radius =16

Find the centre and radius of each of the following circles.
(i) $x^{2} + y^{2} = 25$
(ii) $(x - 5)^{2} + (y - 3)^{2} = 20$
(iii) ${(x - \frac{1}{2})}^{2} + {(y + \frac{1}{3})}^{2} = \frac{1}{36}$